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The hazard matrix with an intervention after 2025: (a) a cohort effect, (b) a period effect. The values correspond to a Weibull distribution W(x;λ=10,k=2)$W( {x;\lambda = 10,k = 2} )$ before the intervention and W(x;12,2)$W( {x;12,2} )$ afterward. Underlying data for this figure can be found in Supporting Information S1.

The hazard matrix with an intervention after 2025: (a) a cohort effect, (b) a period effect. The values correspond to a Weibull distribution W(x;λ=10,k=2)$W( {x;\lambda = 10,k = 2} )$ before the intervention and W(x;12,2)$W( {x;12,2} )$ afterward. Underlying data for this figure can be found in Supporting Information S1.

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Product life extension is often portrayed as one of the pillars of the circular economy since longer lifetimes slow down material turnover rates and thus decrease resource use and associated emissions. Strategies for product longevity can involve addressing the product “nature” (inherent product durability) or “nurture” (external factors). Yet, in...

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... While flows can be more volatile, stocks are generally more stable, reflecting long-term patterns of socioeconomic metabolism (Müller, 2006), given their direct involvement in providing services fulfilling many human needs (Pauliuk & Müller, 2014). Lifetime is usually expressed as a parametric distribution function describing the time delay between inflows and outflows (Baccini & Bader, 1996;van der Voet et al., 2002) or between stocks and outflows (Krych et al., 2024), so it determines the dynamics of the system's stocks and flows. For example, assuming a constant lifetime, if the inflow levels increase, the materials accumulate faster and cause stock growth. ...
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... In this work, we used a time-based approach to lifetime change, which reflects the "nurture" of product lifetimes and can be contrasted with the cohort-based approach, widespread in dMFA, reflecting the "nature" of product lifetimes (Krych et al., 2024). Our time-based perspective means that the lifetime is varied by time, which brings immediate effects on the stock-flow dynamics, allowing us to directly link the lifetime change to other changes in the system, for example, the increase in sales levels. ...
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... This disregards the influence of period effects: external events that can affect multiple cohorts at once during the use phase, such as natural disasters, wars, renovation, or urban policies. However, it is assumed that lifetimes are not only influenced by cohort effects but also by period effects and their combination (Yang & Land, 2013;Krych et al., 2024). To better account for these, the hazard function can be used. ...
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